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<title> BALSAC Version 2.15 Manual, Section 6.2.1</title>
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<h1>6.2.1.  LATTICE OPTION, [L]</h1>

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[L]  This option allows you to select the crystal lattice by defining lattice
     vectors and lattice basis vectors. Several commonly used lattices
     including all 14 primitive Bravais lattices are implemented internally
     and can be selected by key code rather than defining lattice and lattice
     basis vectors. The lattice option menu L reads
 
   ========== LATTICE OPTIONS ==============================================
      Lattice:   title of lattice                (latc)  a=  acon
 
      Select:  [A] sc
               [B] fcc                [L] fcc (Bravais hkl)
               [C] bcc                [M] bcc (Bravais hkl)
               [D] hcp                [N] hcp (lmnq)
               [E] diamond            [O] diamond (Bravais hkl)
               [F] NaCl               [P] NaCl (Bravais hkl)
               [G] CsCl
               [H] zincblende         [Q] zincblende (Bravais hkl)
               [I] graphite           [R] graphite (lmnq)
               [J] free lattice       [S] free lattice (lmnq)
               [K] Bravais lattice
 
               [U]pdate free/Bravais lattice  [V]lattice scaling  [T]itle
               {[X]plot}    [?,]esc
   =================================================================== 50 ==
 
     where the title line gives the title, "title of lattice", of the
     presently selected lattice, the internal lattice code number, latc,
     and the global scaling constant (lattice constant), acon. This line does
     not show if BALSAC/LATTICE was started from scratch and no lattice had
     been defined so far. Further, with BALSAC started from scratch the plot
     option "[X]plot" of this menu is not available and will not be shown.
     The selection of some commonly used lattices is possible from this menu
     by key code input where
 
 &gt;   [A]  selects a simple cubic (sc) lattice.
 
 &gt;   [B]  selects a face centered cubic (fcc) lattice where Miller indices
          are defined with respect to the sc lattice (default for surface
          scientists).
 
 &gt;   [C]  selects a body centered cubic (bcc) lattice where Miller indices
          are defined with respect to the sc lattice (default for surface
          scientists).
 
 &gt;   [D]  selects a hexagonal close packed (hcp) lattice where Miller indices
          are defined with respect to the true reciprocal Bravais lattice.
 
 &gt;   [E]  selects a diamond lattice built of two fcc sublattices where Miller
          indices are defined with respect to the sc lattice (default for
          surface scientists).
 
 &gt;   [F]  selects a sodium chloride, NaCl, lattice built of two fcc
          sublattices where Miller indices are defined with respect to the sc
          lattice (default for surface scientists).
 
 &gt;   [G]  selects a cesium chloride, CsCl, lattice built of two sc
          sublattices where Miller indices are defined with respect to the sc
          lattice (default for surface scientists).
 
 &gt;   [H]  selects a cubic Zincblende, ZnS, lattice (to be used also for GaAs)
          built of two fcc sublattices where Miller indices are defined with
          respect to the sc lattice (default for surface scientists).
 
 &gt;   [I]  selects a graphite lattice built of four hexagonal lattices where
          Miller indices are defined with respect to the true reciprocal
          Bravais lattice.
 
 &gt;   [L]  selects a face centered cubic (fcc) lattice where Miller indices
          are defined with respect to the true reciprocal Bravais lattice.
 
 &gt;   [M]  selects a body centered cubic (bcc) lattice where Miller indices
          are defined with respect to the true reciprocal Bravais lattice.
 
 &gt;   [N]  selects a hexagonal close packed (hcp) lattice where Miller indices
          are given by the hexagonal 4-index notation.
 
 &gt;   [O]  selects a diamond lattice built of two fcc sublattices where Miller
          indices are defined with respect to the true reciprocal Bravais
          lattice.
 
 &gt;   [P]  selects a sodium chloride, NaCl, lattice built of two fcc
          sublattices where Miller indices are defined with respect to the
          true reciprocal Bravais lattice.
 
 &gt;   [Q]  selects a cubic Zincblende, ZnS, lattice (to be used also for GaAs)
          built of two fcc sublattices where Miller indices are defined with
          respect to the true reciprocal Bravais lattice.
 
 &gt;   [R]  selects a graphite lattice built of four hexagonal lattices where
          Miller indices are given by the hexagonal 4-index notation.
 
     The selection of the above lattice types is confirmed by
 
          title of lattice          selected,    code = latc
 
     where "title of lattice" gives the internal lattice name and latc is the
     respective lattice code number, see below. This is followed by a prompt
 
          Global lattice scaling constant  a=
 
     asking for a global lattice constant a to scale all lattice and lattice
     basis vectors (a = 1.0 yields no scaling). This completes the lattice
     definition and BALSAC/LATTICE moves to the Miller index option (main
     option [M]) if the lattice section is built from scratch or returns to
     the BALSAC/LATTICE main option menu.
 
 
 &gt;   [J]  selected from submenu L allows you to define any non-primitive
          lattice in the most general way where lattice plane directions are
          denoted by Miller indices with respect to the reciprocal Bravais
          lattice vectors, see Sec. <a href="./balm.60.html">6.2.3</a>. After a message
 
               free lattice  selected,    code = 10
 
          the prompt
 
               Title of free lattice (A40, "-"=esc) :
 
          asks for a title of the lattice given by an alphanumeric string
          with up to 40 characters (longer names will be truncated). Then the
          three prompts
 
               Lattice vectors :
               R1 = (x1, y1, z1) :
 
               R2 = (x2, y2, z2) :
 
               R3 = (x3, y3, z3) :
 
          ask for cartesian coordinates (x,y,z) (three numbers) of each
          lattice vector, R1, R2, R2, and
 
              No. of lattice basis vectors (&lt;0=rel, &gt;0=abs, 1=primtv, 0=esc):
 
          asks for the number nc of different atoms (described by basis
          vectors, radii and nuclear charges) of the elementary cell of the
          lattice. Here
 
            nc = 1   defines a primitive lattice with one atom (hydrogen)
                     placed at r = (0, 0, 0).
 
               &gt; 0   assumes a non-primitive lattice with nc atoms per unit
                     cell where the following nc prompts
 
                          Input lattice basis (abs:X,Y,Z,RAD,NUC) :
                          Atom  1 ( X, Y, Z, RAD, NUC) :
 
                          ...
 
                          Atom nc ( X, Y, Z, RAD, NUC) :
 
                     ask, for each atom, for five numbers defining absolute
                     cartesian coordinates (x,y,z) of the lattice basis
                     vector, an atomic radius rad, and a nuclear charge nuc.
                     Atomic radii do not need to be known at this point. If
                     (at least) one of the radii is set to zero all rad
                     values are determined as renormalized covalent radii
                     (according to respective nuclear charges nuc, see
                     Sec. <a href="./balm.47.html">5.3</a>). The renormalization is performed such that
                     highest packing without overlapping spheres is achieved.
                     The first atom center will serve as origin of a
                     cartesian coordinate system which is used later on to
                     determine any lattice structure data.
 
               &lt; 0   assumes a non-primitive lattice with |nc| atoms per unit
                     cell analogous to nc &gt; 0. The following |nc| prompts
 
                          Input lattice basis (rel:Q1,Q2,Q3,RAD,NUC) :
                          Atom  1 (Q1,Q2,Q3, RAD, NUC) :
 
                          ...
 
                          Atom nc (Q1,Q2,Q3, RAD, NUC) :
 
                     ask, for each atom, for five numbers (lattice basis
                     vector, atomic radius rad, nuclear charge nuc) analogous
                     to nc &gt; 0. However, the lattice basis vectors are
                     defined in multiples of the lattice vectors
 
                        r = q1 * R1 + q2 * R2 + q3 * R3
 
                     rather than by absolute cartesian coordinates (x, y, z).
 
               = 0   leaves an existing lattice basis vector set unchanged
                     while building a lattice from scratch repeats the above
                     prompt enforcing lattice basis input.
 
          After the lattice basis has been defined BALSAC moves to the
          lattice update menu LU where the atom basis definition can be
          further modified, see [U] of submenu L below.
 
 &gt;   [S]  selected from submenu L is identical to option [J] allowing you to
          define any non-primitive lattice. However, lattice plane directions
          are denoted by Miller indices using the hexagonal 4-index notation
          which is confirmed by the lattice code -10 in the message
 
               free lattice  selected,    code = -10
 
          and becomes useful for non-primitive hexagonal lattices, see
          Sec. <a href="./balm.60.html">6.2.3</a>.
 
 &gt;   [K]  selected from submenu L allows you to define any of the 14
          primitive Bravais lattices which can be updated to include a
          lattice basis for the most general definition of a non-primitive
          lattice. Details of the Bravais lattice option are described in
          Sec. <a href="./balm.57.html">6.2.1.1</a>.
 
 &gt;   [U]  selected from submenu L allows you to update or redefine a free
          lattice definition including Bravais lattices selected before.
          Details of the lattice update option are described in Sec. <a href="./balm.58.html">6.2.1.2</a>.
 
 &gt;   [V]  selected from submenu L has no effect if the lattice is built from
          scratch. Otherwise, BALSAC asks
 
               Global lattice scaling constant  a=
 
          for an updated lattice constant A used to rescale the present
          lattice definition. If A' was the previous lattice constant, all
          lattice and lattice basis vectors and atom radii are scaled by a
          factor A/A'. After this BALSAC returns to the BALSAC/LATTICE main
          option menu.
 
 &gt;   [T]  selected from submenu L has no effect if the lattice is built from
          scratch. Otherwise, the prompt
 
              Title [ ... old title ... ]
              New (A40,"-"=esc) :
 
          shows the present title and asks for a new title (up to 40
          characters, longer text will be truncated). If this prompt is
          answered by the one character title "-" the old title will be kept
          and BALSAC returns to the BALSAC/LATTICE main option menu.
 
 &gt;   [X]  selected from submenu L (not shown and unavailable if the lattice
          is built from scratch) plots the lattice section (switching to
          graphics mode (DOS) or opening a graphics window (Unix)) or
          lists its atom coordinates depending on the plot/list mode defined
          in the graphics option, see Sec. <a href="./balm.64.html">6.2.7</a>.
 
 &gt;   [,]  selected from submenu L returns to the BALSAC/LATTICE startup menu
          if the lattice section is built from scratch. Otherwise BALSAC
          returns to the BALSAC/LATTICE main option menu, see Sec. <a href="./balm.55.html">6.2.0</a>.
 
     After a lattice definition is complete BALSAC/LATTICE moves to the
     Miller index option (main option [M]) if the lattice section is built
     from scratch or returns to the BALSAC/LATTICE main option menu.
 
     In interactive mode, atom sphere radii are constructed as radii of
     touching spheres and may be modified later, see Sec. <a href="./balm.59.html">6.2.2</a>. If the
     lattice option is used with a structure input file values of the atomic
     radii are always read in. If (at least) one of the atomic radii equals
     zero a touching spheres geometry is assumed and all radii are
     recomputed, see also below. For predefined lattices with diatomic bases
     (NaCl, CsCl, cubic ZnS) the ratios of the radii are taken from Coulson's
     tables of ionic radii, see Secs. <a href="./balm.47.html">5.3</a>, <a href="./balm.59.html">6.2.2</a>.
 
     In structure input files code numbers, latc, are used instead of
     characters to denote lattice types. These code numbers are also shown on
     the first line of the BALSAC/LATTICE main option menu and of the lattice
     option menu L. The following table connects option codes used
     interactively in submenu L with lattice code numbers used in structure
     files.
 
         option  code     option  code     option  code     option  code
 
           [A]     1        [B]     2        [C]     3        [D]     4
           [E]     5        [F]     6        [G]     7        [H]     8
           [I]     9        [J]    10        [K]    10        [L]    -2
           [M]    -3        [N]    -4        [O]    -5        [P]    -6
           [Q]    -8        [R]    -9        [S]   -10
 
     NOTE that in structure output files generated by BALSAC/LATTICE all
     structural parameters (lattice vectors, lattice basis vectors, radii)
     are rescaled to a global lattice scaling constant A = 1.0 and A is given
     separately in the first part of the file.
 
 
 
 

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